Increasingly, progress in modern science is being driven by digitized images. This is particularly true in the biological and medical sciences where data takes the form of digital photographs, radiographs, ultrasound images, digital images generated from analytical microassays, and magnetic resonance images, including functional magnetic resonance images.
Functional magnetic resonance imaging (fMRI) is a version of magnetic resonance imaging that identifies local brain activity rather than only structures. Functional magnetic resonance imaging produces two or three dimensional images of activated brain regions based on the detection of the indirect effects of neuroactivity on local blood volume, flow and oxygen saturation. One common form of functional MRI is known as blood oxygen level dependent imaging, or BOLD. The BOLD technique is based on measuring changing ratios of deoxy- and oxy-hemoglobin as a result of increased neuronal metabolic rate and energetic requirements over a period of time. The physiological processes detected using the BOLD technique influence the effective transverse relaxation time of a magnetic resonance (MR) signal which in turn induces activation related signal variations in each volume element of a brain. The overall results are then transformed into a visual output, where active volume elements are rendered by false colors corresponding to the significance of the difference of the dynamic features of the signal in that volume element, as compared to an external reference model.
Unfortunately, many currently available diagnostic digitized images provide only limited diagnostic information. In many cases these images may be evaluated only qualitatively, making it difficult to extract all of the relevant information from the images and to accurately compare or correlate different images. In other cases, the digitized images may be generated using subjective models of the underlying data which may limit the accuracy of the images. For example, the choice of a reference model in the conventional analysis of fMRI data remains arbitrary and subject to systematic and unforeseeable pitfalls, such as those induced by delays or differences in the shape between the MR signal variation and the adopted reference model. Thus, any conclusions drawn from BOLD images so produced will be dependent on the choice of reference model and therefore somewhat subjective.
One analytical technique that has proven successful for the quantitative analysis of linear and non-linear dynamic systems is Recurrence Quantification Analysis (RQA). Recurrence analysis was developed from the original idea by Eckmann et al., that significant periodic structure might be uncovered in physical processes by mathematically embedding the ordered series in higher dimensional space and then creating a rule for determining what is considered a recurrence of a point in the series. These points, then, can be plotted on a symmetric matrix. Deterministic, i.e., non-random, activity can be observed by short line segments parallel to the main diagonal. (See Eckmann et al., Europhys. Lett., 4, 973-976 (1987).) Later, several measures were introduced to quantify features of the RQA plots, including “REC” which quantifies the number of recurrences in a plot and percent determinism (DET) which gives the number of recurrent points which form diagonal line segments in a plot. (See e.g., Zbilut et al., Phys. Lett. A, 171, 199-203 (1992); Webber et al., J. Appl. Physiol., 76, 965-973 (1994); Giuliani et al., Biol. Cybernet., 74, 181-187 (1996); Trulla et al., Phys. Lett. A, 223, 225-260 (1996) and Zak et al., From Instability to Intelligence, Springer, Berlin (1997).)
To date, RQA has focused primarily on dynamic systems. Dynamic systems studied using RQA include studies of respiratory systems, cardiac signals, hearing patterns and brain activity as determined by electroencephalograms (EEGs). In these studies, a time variable signal is measured at two different times (e.g., during and after or before and during an event of interest) and the corresponding RQA variables are calculated for these signals. The temporal distribution of the RQA variables is then analyzed. More recently, RQA has been used to study non-dynamic characteristics of some systems, including protein structure and genetic sequences. (See e.g. Zbilut et al., Protein Engineering, 11, 87-93 (1998) and Frontali et al., Gene, 232, 87-95 (1999).)
RQA has not previously been used to analyze digital images. Nor has RQA been used to provide visual images from a spatial distribution of RQA variables generated from time variable signals collected from a plurality of area or volume elements for a dynamic system.